Answered: An infinitely long conducting…

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter1: Measurement

Section: Chapter Questions

Problem 7E: Write the following quantities in standard units. (a) 0.55 Ms (b) 2.8 km (c) 12 mg (d) 100 cm

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Question

An infinitely long conducting cylindrical rod with a positive charge λ per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of −2λ and radius r1, as shown in the figure.

A) What is E(r), the radial component of the electric field between the rod and cylindrical shell as a function of the distance r from the axis of the cylindrical rod?

Express your answer in terms of λ, r, and ϵ0 the permittivity of free space.

B) What is σ inner, the surface charge density (charge per unit area) on the inner surface of the conducting shell?

C) What is σ outer, the surface charge density on the outside of the conducting shell? (Recall from the problem statement that the conducting shell has a total charge per unit length given by −2λ

D) What is the radial component of the electric field, E(r), outside the shell?